The field of queueing theory has been dedicated to understanding the dynamics of queueing systems and their impact on society. In an age where information is readily available, it is an important problem to understand how information affects the decision making of customers who want to join queueing systems. In some applications, such as amusement parks, transportation systems, and even telecommunication systems, it has been observed that the information given to the customers can potentially be delayed [1]}, [2]}, [3]}, [4]}, [5]}.
This delay in information can be caused by factors such as the fact that it can take time to process and send information about queue lengths to the customers and thus the information that customers actually receive describes the queue lengths from some amount of time in the past. Queueing systems where customers are provided with delayed information have been studied extensively, see for example [6]}, [7]}, [8]}, [9]}, [10]}, [11]}, [12]}, [13]}.
